1. Field of the Invention
The present invention relates to a method for storing membership functions and to a related circuit for calculating a grade of membership of antecedents of fuzzy rules.
2. Discussion of the Related Art
A fuzzy rule is constituted by an antecedent part and by a consequent part or conclusion. The antecedent part has a grade of membership of its own, determined on the basis of a value assumed by inputs and follows semantics of the rule itself.
The antecedent part can be composed of a plurality of terms. In order to determine a weight of an individual term, according to a meaning assumed in fuzzy logic, it is necessary to determine the highest value of an intersection between a membership function and a generic input.
In general, the grade of membership .alpha. is defined as follows:
.alpha.=max.sub.x {min A,A'!}
where A and A' respectively designate the input sets and the corresponding membership function, as shown in FIG. 1.
In the case of crisp inputs, with reference to FIG. 2, the value .alpha. is determined by a segment produced by an intersection between the straight line A defined by the equation UdD=I (where I is the input of the system and UdD is the universe of discourse) and the membership function A'.
Performing this calculation entails using a method for storing the membership function, which has a triangular shape in the example of FIG. 1, so that it is possible to circuitally perform the intersection with the input in the simplest and most economical manner in terms of hardware.
There are various methods for storing membership functions and for their fuzzification. One of these methods consists in storing all the points of the membership function by means of a look-up table.
Another method is the storing of triangular membership functions by means of the gradients and the central vertex of the triangle.
Another method is the storing of trapezoidal membership functions by means of the two vertices and of the distance, relative to the nearest vertex, of the points of intersection between the two sides of the triangle and the axis representing the universe of discourse (UdD), as described in the article "A Parameterized Fuzzy Processor and Its Applications", by B. T. Chen et al., published in the journal "Fuzzy Sets and Systems", Elsevier Science Publishers B.V., no. 59, 1993, pages 149-172.